Jacobi iterations for Canonical Dependence Analysis

In this paper we will study the advantages of Jacobi iterations to solve the problem of Canonical Dependence Analysis. Canonical Dependence Analysis can be seen as an extension of the Canonical Correlation Analysis where correlation measures are replaced by measures of higher order statistical dependencies. We will show the benefits of choosing an algorithm that exploits the manifold structure on which the optimisation problem can be formulated and contrast our results with the joint blind source separation algorithm that optimises the criterion in its ambient space. A major advantage of the proposed algorithm is the capability of identifying a linear mixture when multiple observation sets are available containing variables that are linearly dependent between the sets, independent within the sets and contaminated with non-Gaussian independent noise. Performance analysis reveals at least linear convergence speed as a function of the number of sweeps.

► Canonical Dependence Analysis is an extension of canonical correlation analysis to higher order statistics. ► Jacobi update mechanisms show invariance with respect to initialisation and yield unbiased solutions for population statistics. ► The proposed algorithm resolves the case of mixing matrix estimation for multiple observations of a multivariate contaminated with independent non-Gaussian noise. ► The Jacobi iterations lend themselves to parallel implementation on multicore or multi-processor systems.